DATA602 Assignment 3 Solution

DATA602
In this project you will apply your data wrangling and exploratory data analysis skills to baseball data. In particular, we want to know how well did Moneyball work for the Oakland A's. Was it worthy of a movie?
A bit of background
We'll be looking at data about teams in Major League Baseball. A couple of important points:
Major League Baseball is a professional baseball league, where teams pay players to play baseball. The goal of each team is to win as many games out of a 162 game season as possible. Teams win games by scoring more runs than their adversary. In principle, better players are costlier, so teams that want good players need to spend more money. Teams that spend the most, frequently win the most. So, the question is, how can a team that can't spend so much win? The basic idea that Oakland (and other teams) used is to redefine what makes a player good, i.e., figure out what player characteristics translated into wins. Once they realized that teams were not really pricing players using these characteristics, they could exploit this to pay for undervalued players, players that were good according to their metrics, but were not recognized as such by other teams, and therefore not as expensive.
You can get more information about this period in baseball history from:
Wikipedia
The Moneyball book
The Moneyball movie
The Data
You will be using data from a very useful database on baseball teams, players and seasons curated by Sean Lahman available at http://www.seanlahman.com/baseball-archive/statistics/. The database has been made available as a sqlite database https://github.com/jknecht/baseball-archive-sqlite. sqlite is a light-weight, file-based database management system that is well suited for small projects and prototypes.
You can read more about the dataset here: http://seanlahman.com/files/database/readme2014.txt.
You can download the sqlite file directly from github at https://github.com/jknecht/baseball-archive-sqlite/raw/master/lahman2014.sqlite.
You will be accessing the sqlite database in python using the sqlite package. This package provides a straightforward interface to extract data from sqlite databases using standard SQL commands.
Once you establish a connection with the sqlite database, you can store query results directly in a pandas dataframe using the read_sql function.
For example, here's how you would tabulate total league payrolls for each year:
``` import sqlite3 import pandas sqlite_file = 'lahman2014.sqlite' conn = sqlite3.connect(sqlite_file) salary_query = "SELECT yearID, sum(salary) as total_payroll FROM Salaries WHERE lgID == 'AL' GROUP BY yearID" team_salaries = pandas.read_sql(salary_query, conn) team_salaries.head() ```
The result would look something like:
| | yearID | total_payroll | | --- | --- | --- | | 0 | 1985 | 134401120.0 | | 1 | 1986 | 157716444.0 | | 2 | 1987 | 136088747.0 | | 3 | 1988 |
157049812.0 | | 4 | 1989 | 188771688.0 |
The Question
Part 1: Wrangling
The data you need to answer these questions is in the Salaries and Teams tables of the database.
Problem 1
Using SQL compute a relation containing the total payroll and winning percentage (number of wins / number of games * 100) for each team (that is, for each teamID and yearID combination). You should include other columns that will help when performing EDA later on (e.g., franchise ids, number of wins, number of games).
Include the SQL code you used to create this relation in your writeup. Describe how you dealt with any missing data in these two relations. Specifically, indicate if there is missing data in either table, and how the type of join you used determines how you dealt with this missing data. One note, for SQL you have to be mindful of integer vs. float division.
Part 2: Exploratory Data Analysis
Payroll Distribution
Problem 2
Write code to produce plots that illustrate the distribution of payrolls across teams conditioned on time (from 1990-2014).
Question 1
What statements can you make about the distribution of payrolls conditioned on time based on these plots? Remember you can make statements in terms of central tendency, spread, etc.
Problem 3
Write code to produce plots that specifically show at least one of the statements you made in Question 1. For example, if you make a statement that there is a trend for payrolls to decrease over time, make a plot of a statistic for central tendency (e.g., mean payroll) vs. time to show that specficially.
Correlation between payroll and winning percentage
Problem 4
Write code to discretize year into five time periods (you can use pandas.cut to accomplish this) and then make a scatterplot showing mean winning percentage (y-axis) vs. mean payroll (x-axis) for each of the five time periods. You could add a regression line (using, e.g., NumPy's polyfit) in each scatter plot to ease interpretation.
Question 2
What can you say about team payrolls across these periods? Are there any teams that standout as being particularly good at paying for wins across these time periods? What can you say about the Oakland A's spending efficiency across these time periods (labeling points in the scatterplot can help interpretation).
Part 3: Data transformations
Standardizing across years
It looks like comparing payrolls across years is problematic so let's do a transformation that will help with these comparisons.
Problem 5
Create a new variable in your dataset that standardizes payroll conditioned on year. So, this column for team i in year j should equal:

for team i in year j. where avg_payrollj is the average payroll for year j, and sj is the standard deviation of payroll for year j.
Problem 6
Repeat the same plots as Problem 4, but use this new standardized payroll variable. Question 3
Discuss how the plots from Problem 4 and Problem 6 reflect the transformation you did on the payroll variable.
Expected wins
It's hard to see global trends across time periods using these multiple plots, but now that we have standardized payrolls across time, we can look at a single plot showing correlation between winning percentage and payroll across time. Problem 7
Make a single scatter plot of winning percentage (y-axis) vs. standardized payroll (x-axis). Add a regression line to highlight the relationship.
The regression line gives you expected winning percentage as a function of standardized payroll. Looking at the regression line, it looks like teams that spend roughly the average payroll in a given year will win 50% of their games (i.e. win_pct is 50 when standardized_payroll is 0), and teams increase 5% wins for every 2 standard units of payroll (i.e., win_pct is 55 when standardized_payroll is 2). We will see how this is done in general using linear regression later in the course.
From these observations we can calculate the expected win percentage for team i in year j as

Spending efficiency
Using this result, we can now create a single plot that makes it easier to compare teams efficiency. The idea is to create a new measurement unit for each team based on their winning percentage and their expected winning percentage that we can plot across time summarizing how efficient each team is in their spending.
Problem 8
Create a new field to compute each team's spending effiency, given by

for team i in year j, where expected_win_pct is given above.
Make a line plot with year on the x-axis and efficiency on the y-axis. A good set of teams to plot are Oakland, the New York Yankees, Boston, Atlanta and Tampa Bay (teamIDs OAK, BOS, NYA, ATL, TBA).
Question 4
What can you learn from this plot compared to the set of plots you looked at in Question 2 and 3? How good was Oakland's efficiency during the Moneyball period?
Submission
Prepare and knit an Jupyter notebook that includes for each Problem: (a) code to carry out the step discussed, (b) output showing the result of your code, and (c) a short prose description of how your code works. Remember, the writeup you are preparing is intended to communicate your data analysis effectively. Thoughtlessly showing large amounts of output in your writeup defeats that purpose.
All axes in plots should be labeled in an informative manner. Your answers to any question that refers to a plot should include both (a) a text description of your plot, and (b) a sentence or two of interpretation as it relates to the question asked.
Submit to ELMS at Assignment 3 Submission.